RKPORT ON CAPILLARY ATTRACTION. 287 



Enough has perhaps been said to give an idea of the physical 

 part of M. Poisson's theory ; it remains to notice some of the 

 mathematical deductions obtained from the two principal equa- 

 tions in the succeeding chapters of the work. These equations 

 being the same in form as in Laplace's theory lead to like results. 

 In several instances M. Poisson has carried the mathematical 

 calculation to a greater degree of approximation, and by this 

 means obtained numerical results more nearly agreeing with 

 experiment. Thus, the elevation of the lowest point of the ca- 

 pillary surface in a tube I'^'-goSSl (= -075 in.) in diameter, by 

 the experiments of Gay-Lussac is 15™'- 5861 ; by M. Poisson's 

 calculations 15"''-5829, by those of Laplace 15'"'-5787. 



After extending the analysis to the case in which the interior 

 surface of the tube instead of being cylindrical is any surface 

 of revolution with its axis vertical and its diameter small in the 

 whole extent, M. Poisson considers what will take place when 

 the fluid rises to the upper extremity of the tube, and finds, con- 

 trary to an opinion expressed by Laplace*, that the invariabi- 

 lity of the angle of contact is still maintained under these cir- 

 cumstances, because the radius of curvature of the edge which 

 terminates the interior surface of the tube is always exceedingly 

 greater than the radius of the molecular action. This circum- 

 stance ought to be taken into account in determining the weight 

 necessary to detach a solid disc from the surface of a fluid. 



The weight of a drop of water suspended at the lower extre- 

 mity of a capillary tube and spreading to the exterior edge, is 

 calculated by the theory for the case in which it is just ready to 

 detach itself, and found to be something less than the mean 

 weight of drops falling in succession from the same tube, as in- 

 ferred from an experiment by Gay-Lussac. 



In considering the case of two fluids superincumbent one on 

 the other in the same tube, M. Poisson obtains the same for- 

 mulae as Laplace, and employs them to explain a singular phae- 

 nomenon observed by Dr. Young, and supposed by him to pre- 

 sent an objection to Laplace's theory. Into a capillary tube 

 containing water. Dr. Young inserted a small drop of oil, and 

 then saw the superior surface of the oil depress itself below the 

 original height of the water. This depression, no doubt, refers 

 to the centre of the capillary surface, where it cuts the axis of 

 the tube. If it may be supposed that the oil in descending 

 moistened the tube, and that the water did not wet it originally 

 in its whole extent, the fact is accounted for by the theory. 



The pressure of fluids as modified by capillary action is treated 



* Supplement a la Theorie de l' Action Capillaire, p. 25. 



